Theoretical and Experimental Analysis of the Hydraulic...

Research ArticleTheoretical and Experimental Analysis of the Hydraulic ActuatorUsed in the Active Reflector System

Juliang Xiao Qinyu Liu GuodongWang and Jun Ji

Key Laboratory of MechanismTheory and Equipment Design of Ministry of Education Tianjin University Tianjin 300350 China

Correspondence should be addressed to Juliang Xiao tjxjltjueducn

Received 29 November 2017 Accepted 20 June 2018 Published 26 July 2018

Academic Editor J-C Cortes

Copyright copy 2018 Juliang Xiao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In order to improve the control quality of the active reflector system which is used in the 500 m aperture spherical radiotelescope (FAST) project a study on hydraulic actuator is proposed The dynamic performance of hydraulic actuator is due tothe interaction of several physical phenomena Modeling of such a system needs a unified approach to represent the nonlinearbehavior characteristics Bond graph model is ideal for this task In addition conventional PID control strategy cannot achieve therequired accuracy and precision so we combine grey prediction with PID control Furthermore a new adjustment mechanism ispresented to change the grey step size which is simple automatic less time-consuming and efficient Simulations and experimentson the actuator are carried out to evaluate the effectiveness of the proposed control method In experiments the velocity error is lessthan 005mms and the position error is less than 02mm It shows the actuator meets the astronomical observation requirementtotally

1 Introduction

Five hundred-meter aperture spherical radio telescope(FAST) project belongs to Chinese ldquomegasciencerdquo projectbuilding in the unique karst area which will be the largestsingle aperture radio telescope in the world [1ndash3] It isprimarily composed of active reflector system the support-ing system the measurement and control system and thereceiver and the terminal system As is shown in Figure 1the fundamental surface of active reflector is with a radius of300m caliber of 500m spherical cap surface whose sphericalcap angle is 110 to 120 degrees In order to realize the activedeformation characteristics of radio telescope the supportingstructure of active reflector adopts the cable net structurewhich consists of ring beammain cable net drop-down cablenet triangular reflector unit hydraulic actuator and anchorblock The triangular reflector unit is laid in the main cablenet which is fixed on the beam and the triangle verticesare connected by cable net nodes The drop-down cable netlinks the hydraulic actuator to each node In accordancewith the angle of celestial bodies (S1 and S2) and the real-time shape of active reflector hydraulic actuators adjust thetriangular reflector units position to form a 300m caliber

instantaneous paraboloid in the radio source direction Asa result electromagnetic waves converge on the focusingsurface [4 5]

In the active reflector system it requires small installationspace compact volume large output power and long-termopen-air work of hydraulic actuators And the hydraulicactuator should mainly realize two working conditions

Firstly the actuator changes the observation target whichis the point-to-point motion with a closed-loop velocitycontrol The average velocity is required to reach 16mmsand the velocity error is no more than 005mms Secondlythe actuator traces the observation target in a closed-loopposition control In this situation the position error is lessthan 025mm without velocity requirements

There are two types of hydraulic actuators valve-controlled cylinder [6ndash8] and pump-controlled cylinder [910] The valve-controlled hydraulic actuator with hydraulicservo valve as control unit is gradually replaced by the pump-controlled hydraulic actuator because of its characteristics oflarge throttling loss low efficiency high requirement of oilcleanliness and high price Therefore based on the aboverequirements the hydraulic actuator with the form of pump-controlled differential cylinder is adopted in this paper The

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 8503628 13 pageshttpsdoiorg10115520188503628

2 Mathematical Problems in Engineering

4

R=300m

S1 S2

a 300 m diameter

instantaneous paraboloid

O

F=0467R1

23

56

7

89

120∘

120∘

Figure 1 The optical principle diagram of the active reflectorsystem 1 focusing surface 2 paraboloid 3 spherical surface 4triangular reflector unit 5 main cable net 6 cable net node 7 drop-down cable net 8 hydraulic actuator 9 anchor block

hydraulic actuators mentioned in this paper are all thesekinds of hydraulic actuators

The recent research on pump-controlled differentialcylinder mainly focuses on two aspects of modeling andcontrol strategy

For modeling in [11] the AMESim software is directlyused to model the whole hydraulic system rather thanfocusing on the mathematical description of the systemmodel In [12] a mathematical model of the hydraulic systemis established by state space equations but its research pointis the nonlinearity of friction force and the mathematicalmodel is relatively simple In this paper the hydraulicactuator system is modeled with the method of bond graphwhich not only considers the flow compensation due tothe asymmetry of hydraulic cylinder but also takes thecoupling of several energy domains into account A precisemathematical model of the hydraulic actuator is establishedeffectively

For the control strategy in [13 14] the nonlinear dynamicfeedforward compensation control strategy on the basis ofreforming the flow distribution principle of the pump orusing a special asymmetrical pump is proposed to improvethe dynamic and static performance of the differential cylin-der In [15 16] sliding mode control and robust Hinfin slidingmode control are developed which can achieve accuratetrajectory tracking and effectively resist external interferencebut the control object is the reformed single-rod cylinder notthe differential cylinder Moreover the control signal of slid-ing mode control cannot avoid the chattering which woulddamage themechanical system In [17 18] the neural networkis used as an identifier or a controller to the pump-controlleddifferential cylinder system to accelerate the convergencerate of the tracking error However after each operationthe weights of the neural network need to be updated suchcomplicated calculations make it unsuitable for engineeringpractice In this paper a switching grey prediction PID

control strategy is proposed which is not based on anymodification of system components Besides the interactionof several physical phenomena the uncertainty of the systemparameters the hysteresis and other nonlinear factors areconsidered comprehensively Grey system theory is particu-larly designed for handling situations in which only limiteddata are available especially as the system is not well-definedand fully understoodThe grey prediction technique has beensuccessfully employed to solve many engineering problemsincluding robot position control piezo-actuators positioncontrol which has the inherent hysteresis characteristic anonlinear liquid level system control and boiler drum levelcontrol [19ndash22] Therefore the goal of this control strategyis to apply grey theory to tune up the control parametersMoreover this paper describes a simpler scheme to changethe step size of the grey predictor which not only avoids thecomplexity that the step size is changed by the establishmentof fuzzy rules [23] but also avoids the inaccuracy that the stepsize is changed by step transform threshold set by experience[24]

In this paper the working principle and the integratedstructure of hydraulic actuator are designed for FAST projectSecondly its state space model is established by the methodof bond graphThen a switching grey prediction PID controlstrategy is designed according to the working conditions ofthe hydraulic actuator in the active reflector system In orderto verify the effectiveness of the whole control strategy notonly is simulation carried out on the basis of the bond graphmodel but also a field experiment platform is built in FASTand field tests are conducted

2 Hydraulic System of the Actuator

The hydraulic system is in the form of pump-controlledhydraulic differential cylinder whose working principle isshowed in Figure 2 [25] Apparently the unique system couldnot only meet the movement requirements of active reflectorsystem just by controlling the rod chamber of differentialhydraulic cylinder but also allow a variable transmissionof power by connecting a pump directly to an actuator[26]

21 Working Principle of Installation and Commissioning

211 Automatic Adjustment In this case there is no-loadAs the piston rod extends out the solenoid valves (DC1and DC2) are energized and the motor is reversed (counter-clockwise) so the rod chamber is connected to the nonrodchamber The oil supplied by the pump is combined withthe oil from rod chamber and then flows into the nonrodchamber to realize the output of the piston rod by usingdifferential output structure

When the piston rod is retracted DC1 and DC2 are offwhile the motor is also reversed The oil flows from the oiltank to the rod chamber passing through the pump and YDFOil in nonrod chamber flows back to the oil tank

212 Manual Adjustment In the absence of electricity thepiston rod can be extended or retracted at a certain speed

Mathematical Problems in Engineering 3

1

4

5

2

6Y1

Controller

8

TriangularReflector

Unit

B A

M

P

YL1

YL2

DC1 DC2

YDF

YL3

DF3 DF1 DF2 DF4

S2

S1

3

KB

7

9

drop-down cable net

FL

Figure 2The hydraulic schematic diagram of hydraulic actuator 1 hydraulic differential cylinder 2 displacement sensor 3 pressure sensor4 bidirectional quantitative gear pump 5 two-phase hybrid stepping motor 6 oil tank 7 temperature sensor 8 electric control system 9hand pump DC1 andDC2 solenoid valves YL1 relief valve YL2 overflow valve YL3 counterbalance valve YDF pilot operated check valveDF1 DF2 DF3 and DF4 check valves S1 and S2 quick-change connector KB pressure joints Y1 filter

to meet the commissioning needs by using quick-changeconnector and hand pump

22 Working State In this case the actuator is pulled bythe triangular reflector unit solenoid valves (DC1 and DC2)are off all the time and the nonrod chamber is connectedto the tank When the piston rod extends out the externalload is driving force On the contrary the external load isresistance when the piston is retractedThe system can realizethe automatic correction and compensation in a closed-loopcontrol condition while the velocity and position signals ofthe piston rod are fed back to the electrical control systemthrough the sensor

As the piston rod extends out themotor is clockwise andthe outlet pressure of the gear pump is increasing When thepressure reaches the set pressure of YL3 the YDF opensWiththe external load the oil flows from the rod chamber to thenonrod chamber via the YDF gear pump and YL3 Becausethe two chamber areas are different the compensatory oilflowing into the nonrod chamber is from the tank

When the piston is retracted the motor is reversed theoil is transported to the rod chamber by the gear pump andthe oil in nonrod chamber flows back to the tank

23 Integrated Structure The mechanical structure ofhydraulic actuator is shown in Figure 3 The integrated valve

block consists of solenoid valve relief valve overflow valvecounterbalance valve pilot operated check valve checkvalves filter quick-change connector power supply andcommunication interface which not only optimizes thelayout of the components but also saves the volume Theswitch power supply is a low voltage DC and the electricprotective cover is made of die cast aluminum To effectivelyrestrain the temperature rise the heat conducting pipes arearranged on the electric machine to carry out auxiliary heatradiation

The hydraulic actuator does not require extra equipmentsuch as oil pipelines and large external control system Elec-trical control part is arranged in the motor terminal supportand the displacement sensormounted on the cylinder bottomfeeds back position signal to the controller In additionsealing structure makes the oil avoid the external pollutionand improves the adaptability of the actuator

24 System Block Diagram System block diagram is illus-trated in Figure 4 which can also be called the hardware flowchart of the closed-loop control system In normal workingcondition external power supply provides electricity for sys-tem by the filter installed in the hydraulic actuator externalcontrol signal is delivered to control port by fiber interfaceClosed-loop control of the hydraulic system is implementedby the displacement sensor while the temperature signal and


12

3 4 5 6 7 8 9 10

15

11 12

1314

Figure 3 Hydraulic actuator structure 1 hydraulic differential cylinder 2 displacement sensor 3 oil tank 4 air float 5 gear pump 6integrated valve block 7 power interface 8 wave filter 9 temperature andpressure sensor 10 two-phase hybrid steppingmotor 11 controller12 electric protective cover 13 switching power supply 14 motor driver 15 solenoid valve

external input signal

Interface_2

Fiber interface

AC

filter

object instruction

solenoid valve

temperature and pressure transmitter

displacement sensor

Interface_1

Interface_3

Interface_4

CPUSTM

32F103Motor driving

interface motor driver

stepping motor

coupling

gear pump

differential cylinder

piston rod

external load

the temperature of

electrical chamber

the temperature

and pressure of oil

signal acquisitiondisplacement signal

Figure 4 System block diagram

pressure signal are just regarded as warning signals to ensurethe security of the system

3 Dynamic Bond Graph Model of the System

Modeling an actuator system is a complex process Thereasons are as follows

First of all the hydraulic actuator is a nonlinear anduncertain system due to the asymmetry of differential cylin-der and the influence of environmental temperature onthe hydraulic fluid bulk modulus and the hysteresis [27]Secondly the hydraulic actuator system has the couplingof several energy domains (mechanical electrical hydrody-namic etc) [28ndash31]Moreover traditionalmodelingmethodssuch as transfer functions cannot meet the requirements ofmodeling a multi-input system Finally for this hydraulicactuator six state variables need to be selectedwhilemodeling

by the state equations directly However the selection ofso many state variables is very difficult Hence the bondgraph approach is proposedwhich can decompose the systeminto subsystems to exchange energy The global state spaceequation can be established accurately by this method

In the bond graph 0-Junction is a common effort junc-tion which relates effort variables at one point 1-Junctionis a common flow junction which relates flow variables atone point 119879119865 is a converter which describes a transforma-tion relationship between two effort variables or two flowvariables in the process of energy transfer 119866119884 is a gyratorwhich describes a transformation relationship between effortvariables and flow variables in the process of energy transfer

The systemrsquos main power flows are shown in Figure 5

31 Bond Graph Model of the Stepping Motor Essentiallytwo-phase hybrid stepping motor is low speed salient pole


Stepping Motor

Gear Pump

Hydraulic Cylinder LoadElectric

PowerMechanical

PowerHydraulic

Power

Voltage (cause)

Torque (effect)

Pressure (effect)

Force (cause)

Current (effect)

Angular Velocity (cause)

Volumetric Flow (cause)

Velocity (effect)

Effort variables

Flow variables

Mechanical Power

Figure 5 The power flows

permanentmagnet synchronousmotorTherefore the designof the hybrid stepping motor servo system can consult withthe experience of the permanent magnet synchronous servosystem [32 33]

The voltage balance equation is shown as follows

119880119860 = 119877119894119860 + 119871119889119894119860119889119905 minus 119911119903Φ119898120596119890 sin (119911119903120579119903)119880119861 = 119877119894119861 + 119871119889119894119861119889119905 + 119911119903Φ119898120596119890 cos (119911119903120579119903)

(1)

where 119880119860 and 119880119861 represent the stator voltage of A axis andB axis respectively 119877 is the winding resistance 119871 is theinductance coefficient of winding 119894119860 and 119894119861 are the currentin winding 119911119903 is the rotor teeth number Φ119898 is the magneticflux of permanent magnet 120596119890 is the electric angular velocityof the rotor and 120579119903 is the angular displacement of the rotor

The electromagnetic torque equation is

119879119890 = minus119911119903Φ119898119894119860sin (119911119903120579119903) + 119911119903Φ119898119894119861cos (119911119903120579119903) (2)

The mechanical motion equation is

119879119890 = 119869119898 11988921205791199031198891199052 + 119861119898 119889120579119903119889119905 + 119879119871 (3)

where119879119871 is the load torque 119869119898 is the moment of inertia of therotor 119861119898 is the viscous friction coefficient

The bond graph of the motor with the electrical lossand mechanical loss into consideration is shown in Figure 6where 1198721198781198901 is the effort variable on the input port 119877119891 is theinternal resistance caused by the viscous friction of themotor(ie 119877119891 = 1B119898) 119896119890 is the torque coefficient (ie 119896119890 = 119911119903Φ119898)119879119900119906119905 is the output torque and 120596119900119906119905 is the output speed32 Bond Graph Model of the External Gear Pump Thediagram of gear pump is shown in Figure 7

Define 119899 as the rotation speed of the pump and 119881119905 as thedisplacement of the pump 119901119894119899 119876119894119899 119901119900119906119905 and 119876119900119906119905 are thepressure and flow of the pump inlet and outlet respectivelyand Δ119901 is the pressure difference

RL fR

1MSe GY

mJ

outT

out

(ke)Figure 6 The model of two-phase hybrid stepping motor

inQinp

outQoutp

tVn

T

Δp=poutminuspin

Figure 7 The diagram of gear pump

The flow equation of gear pump is

119876 = 119899119881119905 minus 119885VΔ119901 minus 119862V119889 (Δ119901)

119889119905119885V = 100381610038161003816100381610038161003816100381610038161003816

120597119876120597 (Δ119901)

100381610038161003816100381610038161003816100381610038161003816(4)

where 119885V is the internal leakage coefficient 119862V is the liquidcapacity of the pump working chamber

The torque equation of gear pump is

119879 = (11989631015840 + 1198811199052120587) Δ119901 minus 119887119899119899 minus 2120587119869119875119889119899119889119905

119887119899 = 120597119879120597119899

(5)


10MSe2

vRvC pL pR

outP

outQTF1

inT1

J wp R

(Vt2)in

Figure 8 The model of external gear pump

epC

epCipC

1A

2A

1p

2p 1Q

2Q

px

lF

Figure 9 The diagram of hydraulic differential cylinder

where 11989631015840 is the torque loss coefficient because of the pressure119887119899 is the linearization coefficient and 119869119875 is the moment ofinertia of the pump

According to the equivalent of hydraulic power andmechanical power the linear motion equation of pump canbe obtained

Δ119901119901 = 119870119901Δ119901 minus 119877119901119876119905 minus 119871119901 119889119876119905119889119905 (6)

where Δ119901119901 is the actual pressure difference during the pumpworking 119870119901 = 21205871198963119881119905 1198963 = 11989631015840 + 1198811199052120587 119877119901 = 21205871198871198991198811199052119871119901 = 119869119901 sdot (2120587119881119905)2 and 119876119905 is theoretical flow (ie 119876119905 = 119899119881119905)

The bond graph of the external gear pump is establishedbased on the above equations which is shown in Figure 8 Inthismodel1198721198781198902 is the effort variable on the input port of thegear pump 119879119894119899 is the input torque 120596119894119899 is the input angularvelocity 119875119900119906119905 is the output pressure 119876119900119906119905 is the output flowrate 119877119908 is internal resistance caused by rotational resistanceloss of the pump 119877V is internal resistance caused by internalleakage of the pump (ie 119877V = 1119885V)

33 Bond Graph Model of the Hydraulic Cylinder Theschematic diagram of hydraulic differential cylinder is shownin Figure 9

Considering the compressibility of the hydraulic fluidand leakage in the hydraulic differential cylinder the flowequation can be obtained

1198761 = 1198601119901 + 119862119894119901 (1199011 minus 1199012) + 1198621198901199011199011 + 11988111205731198901198891199011119889119905

1198762 = 1198602119901 + 119862119894119901 (1199011 minus 1199012) minus 1198621198901199011199011 minus 11988121205731198901198891199012119889119905

(7)

where 1198761 and 1198762 are the flow of the rod chamber and nonrodchamber11990111198601 and11990121198602 are the pressure and effective areaof the rod chamber and nonrod chamber respectively 119862119894119901119862119890119901 are the internal leakage coefficient and external leakage

10inP

inQMSf

dC

tR

TF2

bR

m1s

F

pv0

(A2)Se

Figure 10 The model of hydraulic differential cylinder

coefficient of the cylinder 1198811 and 1198812 are the liquid volume ofthe rod chamber and nonrod chamber120573119890 is the bulkmodulusof hydraulic fluid 119909119901 is the displacement of the piston rodThe pressure of nonrod chamber is close to zero because it isconnected to the tank all the time so we define that 1199012 = 0Assuming that the initial volume of rod chamber is zero 119871 119904 isthe stroke of hydraulic cylinder and 1198811 1198812 can be simplifiedto

1198811 = 11986011199091199011198812 = 1198602 (119871 119904 minus 119909119901) (8)

The force balance equation of the hydraulic cylinder is

11990111198601 minus 11990121198602 = 119898119901 + 119861119887119901 + 119865119897 (9)

where 119898 is the total mass which consists of the piston massand the reduced mass delivered by the load 119861119887 is the totalviscous damping coefficient and119865119897 is the pull of the cable net

From the above equations we can get the bond graph ofthe hydraulic cylinder which is shown in Figure 10

In the model of hydraulic cylinder 119872119878119891 is the input flowvariable119875119894119899 is the input pressure119876119894119899 is the input flow119865 is theoutput force V119901 is the output velocity 119878119890 is force source whichis the pull of the cable net 119877119887 is internal resistance caused byviscous damping (ie 119877119887 = 1119861119887) 119877119905 is internal resistance


1 0

dC

tR

TF2

bR

m

Se

1s

F

pv0

10

vRvC pL

pRTF1

RLfwR

MSe1 GY

J

1

2 3

4 5

6 7

8 9

10

12

1113

14

16

17

1819

20

21

2223

11

Load Hydraulic Cylinder

Motor Pump

ASRController

15

P

Q

SensorA

OB

Feedback SignalDisplacement

Velocity

Target Value

+ +

minusminus

g

f

(A2)

(ke) (Vt2)

Figure 11 Closed-loop control system model of hydraulic actuator

caused by the internal leakage and external leakage of thecylinder (ie 119877119905 = 1(119862119894119901 + 119862119890119901)) 119862119889 is the liquid capacity ofthe rod chamber When the piston rod is at the midpoint ofthe hydraulic cylinder the stability was worst so we computeliquid capacity based on midpoint The liquid capacity 119862119889(119905)of the rod chamber at the time 119905 is

119862119889 (119905) = (1198601 sdot 119871 1199042 minus 1198601 sdot int V119901 (119905) 119889119905)120573119890 (10)

34 Global System Modeling In summary the bond graphmodel of the system can be integrated into the form whichis shown in Figure 11 where 119869 is the total moment of inertiaof the motor rotor and the pump 119877119891119908 is the total resistanceloss coefficient of motor and pump The voltage of the motor1198721198781198901 is controlled by the automatic speed regulator (ASR)while the essence of ASR is the PI regulator whose input is thedifference value of target angular velocity and output angularvelocity According to the principle of stepping motor thefollowing equation shows the relationship between the pulsefrequency and the angular displacement

120579119894 (119905) = 119870120579 sdot int 119891 (119905) 119889119905 (11)

where 119891(119905) represents the pulse frequency function and 119870120579represents the step angle of the stepping motor Thereforewe can control the angular displacement and the rotationvelocity of stepping motor by controlling 119891(119905)35 State Equation Expression of the System The systemis multiple input single output system which contains sixenergy storage elements Two inputs are respectively 1198721198781198901and 119878119890 the output is V119901 According to the characteristicequation of every energy storage element and the constraint

equation of each node mathematical equation can be estab-lished as follows

2 = 1198721198781198901 minus 119877119871 1198752 minus 119896119890119869 11987566 = 119896119890119871 1198752 minus 119877119891119908119869 1198756 minus 1198811199052120587119862V

1198811010 = 11988111990521205871198691198756 minus 1119862V119877V

11988110 minus 11198711199011198751313 = 1

119862V11988110 minus 11987711990111987111990111987513 minus 1

1198621198891198811616 = 1

11987111990111987513 minus 111986211988911987711990511988116 minus 1198602119898 11987520

20 = 119860211986211988911988116 minus 119877119887119898 11987520 minus 119878119890

(12)

The 6 state variables are respectively the generalizedmomentum 1198752 at bond 2 the generalized momentum 1198756at bond 6 the generalized displacement 11988110 at bond 10the generalized momentum 11987513 at bond 13 the generalizeddisplacement 11988116 at bond 16 and the generalized momentum11987520 at bond 20

The state space expression of the system is

(119905) = 119860 (119905) sdot 119883 (119905) + 119861 (119905) sdot 119880 (119905)119884 (119905) = 119862 (119905) sdot 119883 (119905) + 119863 (119905) sdot 119880 (119905) (13)

where 119883(119905) = [1198752 1198756 11987513 11987520 11988110 11988116]119879 is state variable119880(119905) = [1198721198781198901 119878119890]119879 is input variable and 119884(119905) = [V119901] isoutput variable


ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1

Se OutputΣ(A(t)B(t)C(t)D(t))

X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus

Figure 12 Computer simulation model of hydraulic actuator

In the system the state matrix119860(119905) input matrix 119861(119905) theoutput matrix 119862(119905) and direct coupling matrix 119863(119905) are

119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889

0 0 0 minus119877119887119898 0 11986021198621198890 1198811199052120587119869 minus 1119871119901 0 minus 1119862V119877V0

0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)

As a result the global systemmodeling of the closed-loopsystem can be expressed as in Figure 12 which is simple andconvenient

4 System Controller

41 Schematic of Switching Grey Prediction PID Control Asshowed in Figure 13 the control principle of the switchinggrey prediction PID (SGPID) control is achieved throughadding the grey prediction model into the feedback loop ofPID controller

If 119884(0)(119905) is the sampling value at time 119905 the equal-dimensional new information sequence composed of themost recent 119899 data is described by

119884(0) = (119884(0) (119905 minus 119899 + 1) 119884(0) (119905 minus 119899 + 2) sdot sdot sdot 119884(0) (119905)) (15)

According to the metabolic principle the equal dimen-sion new information GM (1 1) model is constructed [34]The 119898 step forecasting output of the system is

(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887

119886] (1 minus 119890119886) 119890minus119886(119905+119898minus1) (16)

where 119886 and 119887 are the development coefficient and the greyinput coefficient 119898 is the forecasting step size In industrialcontrol the dimension of the sequence for constructingequal-dimensional new information GM (1 1) model is nottoo large usually 119899 = 5

The forecasting step size119898 has a prominent impact on thecontrol effect of the grey prediction PID control system Inorder to improve the performance of the controller furthera new step adjustment mechanism is introduced to changethe step size of the grey predictor It can adjust the stepsize automatically according to the prediction error 119890(119905) theactual error 119864(119905) and the rate of actual error change 119864119862(119905)42 Step Adjustment Mechanism (SAM) As showed inTable 1 if 119890(119905) sdot 119864(119905) lt 0 it indicates that the output of thesystem is close to the set value thus the absolute value of theforecasting step should be a smaller value in order to avoidovershoot On the contrary when 119890(119905) sdot 119864(119905) ge 0 it shows thatthe output is seriously deviated from the set value and theactual error is large so the absolute value of the forecastingstep should be a larger value

5 Simulation and Analysis

In order to verify the effectiveness of the whole control strat-egy the simulation is carried out using MATLAB softwareThe global state space equation obtained by bond graph isadopted as the systemmathematical model in the simulationAssuming that the initial position of the piston rod is atthe midpoint of the hydraulic cylinder when the piston rodextends out the displacement is the positive The quality ofthe triangular reflector unit is 7000kg the displacement ofthe gear pump is 10 times 10minus6m3r the diameter of piston rod is60mm the diameter of hydraulic cylinder is 100mm and thestroke of hydraulic cylinder is 1200mm


Table 1 Step adjustment strategy

119864119862(119905) The judgment criterion 119864(119905) Control Mode 119898

119864119862(119905) lt 0 the response ofthe system is in the risingphase

119890(119905) sdot 119864(119905) lt 0 the output is close tothe target

119864(119905) ge 0 the output is close to thetarget

rise slowlyto avoid overshoot 1

119864(119905) lt 0 the output slightly exceedsthe target restrain overshoot 2

119890(119905) sdot 119864(119905) ge 0 the output isseriously deviated from the target

119864(119905) ge 0 the output is greatly lowerthan the target

rise rapidlyto reduce rise time -2

119864(119905) lt 0 the output greatly exceedsthe target down rapidly 3

119864119862(119905) gt 0 the response ofthe system is in the declinephase


119864(119905) ge 0 the output slightly exceedsthe target restrain overshoot 2

119864(119905) lt 0 the output is close to thetarget

down slowlyto avoid overshoot 1


119864(119905) ge 0 the output greatly exceedsthe target rise rapidly 3

119864(119905) lt 0 the output is greatly lowerthan the target

down rapidlyto reduce fall time -2

119864119862(119905) = 0 the response ofthe system is in thestationary phase

ndash Constant keep steady to avoid thestatic error and oscillation 1

HydraulicActuator

Step Adjustment Mechanism

GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)

Figure 13 The schematic diagram of SGPID

51 Simulation of Changing the Target Source In this con-dition the switch OB in Figure 11 switches on to realizethe velocity closed-loop control of the system In order toachieve the point-to-point changing source movement of thepiston rod and make piston rod move between 280mm and600mm the square wave signal whose amplitude is 16mmsand period is 400s is given to the system to simulate two kindsof state of velocity signal (ie minus16mms and+16mms)Thedisplacement of piston rod is shown in Figure 14(a)

Two different strategies are simulated under the samecontrol parameters (119870119901 = 226 119870119894 = 095 and 119870119889 = 016)With the PID control strategy and the SGPID control strategyapplied to the hydraulic system the velocity curve and thevelocity error curve are separately given in Figures 14(b) and14(c)

When the piston rod is retracted from 600mm to 280mmat a speed of minus16mms two kinds of control strategies canmaintain velocity response without oscillation However thevelocity controlled by PID strategy appears with apparentdelay in other words response time is longer and its velocityerror is less than 02mms On the contrary SGPID strategy

Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)

Figure 14 Simulation of changing the source condition

has a quick response and the velocity error has reduced to lessthan 0048mms

As the piston rod extends out from 280mm to 600mmat a speed of +16mms the velocity controlled by PIDstrategy appears with obvious oscillation and overshoot and


Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)

Figure 15 Simulation of the scanning tracking condition

Controller

Solenoid valve DC1

Switching power supply

Stepping motor and driver

Solenoid valve DC2

Integrated valve block

Oil tank

Figure 16 Field experiment

the velocity error is about 033mms In contrast the velocityerror controlled by SGPID strategy reduced to 005mmswithno velocity oscillation

Overall the velocity error of PID strategy is too largewhile SGPID strategy makes the velocity error remain within005mms which meets the requirement of FAST project

52 Simulation of Scanning Tracking In order to simulate theworking condition of the active reflector system tracking thetarget the switch OA in Figure 11 switched on to realize theposition closed-loop control of the system The approximateequation of the target curve is obtained by fitting the datawhich can be expressed as

119910 = minus1627 times 104 + 1303 times 104 sdot cos (120596119905) + 2098times 104 sdot sin (120596119905) + 4398 sdot cos (2120596119905) minus 8900sdot sin (2120596119905) minus 1293 sdot cos (3120596119905) + 1257 sdot sin (3120596119905)+ 1293 sdot cos (4120596119905) + 1691 sdot sin (4120596119905)

(17)

The target curve is shown in Figure 15(a) where 120596 =211375rads Similarly with the two control strategiesapplied to the hydraulic system under the same controlparameters (119870119901 = 5019 119870119894 = 19 and 119870119889 = 072) theposition error curve is shown in Figure 15(b)

Therefore the position tracking error controlled by PIDstrategy is within 06mm but SGPID control strategy canmake it remain within 018mm which greatly improves thetracking accuracy

6 Experimental Study

In order to verify the working performance of the hydraulicactuator a field experiment is carried out to compare thecontrol effects of PID strategy and SGPID strategy which isshown in Figure 16 The internal structure of the actuator isillustrated in subfigure A and subfigure B

61 Experiment of Changing the Target Source Velocity con-trol of the piston rod is achieved by the velocity closed-loop control of the system so that the piston rod realizesthe point-to-point movement at speed of minus16mms and


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)

Figure 17 The control effect of PID

0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)

Figure 18 The control effect of SGPID

0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)

Figure 19 Experiment of the scanning tracking condition

speed of +16mms Figure 17 is the control effect of thehydraulic actuator under PID strategy When the piston rodis retracted at a speed of minus16mms the velocity responseis rapid but it oscillates at the early stage the velocity erroris about 02mms As the piston rod extends out at a speedof +16mms the velocity appears with obvious fluctuationoscillation and overshoot and the velocity error is about04mms

In contrast control effect of SGPID strategy is shownin Figure 18 There is no overshoot and fluctuation thevelocity error is reduced to less than 005mmsTherefore theexperiment proved that SGPID control strategy can improvethe performance of the actuator effectively

62 Experiment of Scanning Tracking The hydraulic actuatorrealizes scanning tracking by the position closed-loop controlof the systemThe experimental result of scanning tracking isshown in Figure 19 It shows that the fluctuation amplitude ofthe position error is large (about 075mm)under PID strategybut the position error controlled by SGPID strategy is within02mm whose stability is improved significantly

7 Conclusion

The article presents an integrated study approach aboutmod-eling analysis and simulation of a new closed-loop pump-controlled differential hydraulic cylinder system which is


specially applied to the five hundred-meter aperture sphericalradio telescope project

The bond graph model of the complete system hasbeen developed Combining the pump-controlled differentialcylinder with a motor circuit the dynamic response ofthe closed-loop system is analyzed To achieve the desiredperformance of the system with respect to the changing thetarget source condition and the scanning tracking condi-tion a suitable controller named SGPID is designed whoseadjustment mechanism is very convenient for engineeringapplication The close agreement between the experimentresult and the simulation result validates the appropriatenessof the proposed model and the effectiveness of adjustmentmechanism of SGPID

The results indicate that the SGPID control strategyis able to eliminate and reduce the velocity fluctuationand oscillation Meanwhile both the velocity error and theposition error are controlled within a required range It notonly improves the dynamic performance of the hydraulicactuator but also provides good protection for the normalwork of the active reflector system

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

This paper is supported by the Tianjin Science and TechnologySupporting Key Projects (16YFZCGX00820)The authorswishto acknowledge the URANUS Hydraulic Machinery Co LtdChina for providing fund in this research Thanks are due toall the members of laboratory for providing help during thedevelopment of this research

References

[1] R Nan D Li C Jin et al ldquoThe five-hundred-meter aperturespherical radio telescope (FAST) projectrdquo International Journalof Modern Physics D vol 20 no 6 pp 989ndash1024 2011

[2] D Li R Nan and Z Pan ldquoThe five-hundred-meter aperturespherical radio telescope project and its early science oppor-tunitiesrdquo Proceedings of the International Astronomical UnionNeutron Stars and Pulsars Challenges and Opportunities after80 Years vol 8 no 291 pp 325ndash330 2012

[3] X Tang and Z Shao ldquoTrajectory generation and trackingcontrol of a multi-level hybrid support manipulator in FASTrdquoMechatronics vol 23 no 8 pp 1113ndash1122 2013

[4] J Xiao J Ji Y Yao B Liu J Zhang and Z Bai ldquoApplicationof grey predictor based algorithm to hydraulic actuator usedin FAST projectrdquo Tianjin Daxue Xuebao (Ziran Kexue yuGongcheng Jishu Ban)Journal of Tianjin University vol 49 no2 pp 178ndash185 2016

[5] Ji Jun Development and Performance Analysis of the HydraulicActuator Used in the Active Reflector System of the FAST ProjectMaster Thesis Tianjin University Tianjin 2016

[6] Xin Zuo Jian-wei Liu Xin Wang and Hua-qing LiangldquoAdaptive PID and Model Reference Adaptive Control Switch

Controller for Nonlinear Hydraulic Actuatorrdquo MathematicalProblems in Engineering vol 2017 Article ID 6970146 15 pages2017

[7] E Kolsi-Gdoura M Feki and N Derbel ldquoObserver BasedRobust Position Control of a Hydraulic Servo System UsingVariable Structure Controlrdquo Mathematical Problems in Engi-neering vol 2015 Article ID 724795 11 pages 2015

[8] Jianyong Yao Guichao Yang and Dawei Ma ldquoInternal LeakageFault Detection and Tolerant Control of Single-Rod HydraulicActuatorsrdquo Mathematical Problems in Engineering vol 2014Article ID 345345 14 pages 2014

[9] G K D H Z C C Minglan ldquoProgress of the human-vehicle closed-loop system manoeuvrailityrsquos evaluation andoptimizationrdquo Chinese Journal of Mechanical Engineering vol39 pp 27ndash35 2003

[10] L Quan F Li H Tian and Z Yan ldquoPrinciple and applicationof differential cylinder system controlled with displacementpump accumulator and proportional valverdquo Jixie GongchengXuebaoChinese Journal of Mechanical Engineering vol 42 no5 pp 115ndash119 2006

[11] A E Alemu and Y Fu ldquoSliding mode control of electro-hydrostatic actuator based on extended state observerrdquo inProceedings of the 29th Chinese Control andDecision ConferenceCCDC 2017 pp 758ndash763 China May 2017

[12] Y Lin Y Shi and R Burton ldquoModeling and robust discrete-time sliding-mode control design for a fluid power electrohy-draulic actuator (EHA) systemrdquo IEEEASME Transactions onMechatronics vol 18 no 1 pp 1ndash10 2013

[13] LQuan ldquoCurrent state problems and the innovative solution ofelectro-hydraulic technology of pump controlled cylinderrdquo JixieGongcheng XuebaoChinese Journal of Mechanical Engineeringvol 44 no 11 pp 87ndash92 2008

[14] H Zhao H Zhang L Quan and B Li ldquoCharacteristicsof asymmetrical pump controlled differential cylinder speedservo systemrdquo Jixie Gongcheng XuebaoJournal of MechanicalEngineering vol 49 no 22 pp 170ndash176 2013

[15] W Shen Y Pang and J Jiang ldquoRobust controller design of theintegrated direct drive volume control architecture for steeringsystemsrdquo ISA Transactions vol 78 pp 116ndash129 2018

[16] H Zhang X Liu J Wang and H R Karimi ldquoRobust 119867infinsliding mode control with pole placement for a fluid powerelectrohydraulic actuator (EHA) systemrdquo The InternationalJournal of Advanced Manufacturing Technology vol 73 no 5-8 pp 1095ndash1104 2014

[17] Q Gao L-J Ji Y-L Hou Z-Z Tong and Y Jin ldquoModelingof electro-hydraulic position servo system of pump-controlledcylinder based on HHGA-RBFNNrdquo in Proceedings of the 2011International Conference on Electronics Communications andControl ICECC 2011 pp 335ndash339 China September 2011

[18] E Kilic M Dolen H Caliskan A Bugra Koku and T BalkanldquoPressure prediction on a variable-speed pump controlledhydraulic system using structured recurrent neural networksrdquoControl Engineering Practice vol 26 no 1 pp 51ndash71 2014

[19] E Kayacan and O Kaynak ldquoGrey prediction based control of anon-linear liquid level system using PID type fuzzy controllerrdquoin Proceedings of the 2006 IEEE International Conference onMechatronics ICM pp 292ndash296 Hungary July 2006

[20] J Lin H Chiang and C C Lin ldquoTuning PID control param-eters for micro-piezo-stage by using grey relational analysisrdquoExpert SystemswithApplications vol 38 no 11 pp 13924ndash139322011


[21] E Kayacan and O Kaynak ldquoAn adaptive grey PID-type fuzzycontroller design for a non-linear liquid level systemrdquo Transac-tions of the Institute of Measurement amp Control vol 31 no 1 pp33ndash49 2009

[22] N Yu W Ma and M Su ldquoApplication of adaptive Greypredictor based algorithm to boiler drum level controlrdquo EnergyConversion and Management vol 47 no 18-19 pp 2999ndash30072006

[23] D Q Truong and K K Ahn ldquoForce control for hydraulicload simulator using self-tuning grey predictor - fuzzy PIDrdquoMechatronics vol 19 no 2 pp 233ndash246 2009

[24] Xiao Juliang Wang Guodong Yan Xiangan et al ldquoSwitchinggrey prediction fuzzy control research and applicationrdquo Journalof Tianjin University vol 40 no 7 pp 859ndash863 2007

[25] Tianjin Uranus Hydraulic Machinery Co Ltd ldquoHydraulicActuatorrdquo China Patent No103307059A Sep 18 2013

[26] SHabibi ldquoDesign of a newhigh-performance ElectroHydraulicActuatorrdquo IEEEASME Transactions on Mechatronics vol 5 no2 pp 158ndash164 2000

[27] K K Ahn D N C Nam and M Jin ldquoAdaptive backsteppingcontrol of an electrohydraulic actuatorrdquo IEEEASME Transac-tions on Mechatronics vol 99 pp 1ndash9 2013

[28] G Sun and M Kleeberger ldquoDynamic responses of hydraulicmobile crane with consideration of the drive systemrdquo Mecha-nism and Machine Theory vol 38 no 12 pp 1489ndash1508 2003

[29] K Dasgupta J Watton and S Pan ldquoOpen-loop dynamicperformance of a servo-valve controlled motor transmissionsystem with pump loading using steady-state characteristicsrdquoMechanism and Machine Theory vol 41 no 3 pp 262ndash2822006

[30] P Athanasatos and T Costopoulos ldquoProactive fault finding ina 43-way direction control valve of a high pressure hydraulicsystem using the bond graph method with digital simulationrdquoMechanism and Machine Theory vol 50 pp 64ndash89 2012

[31] K Dasgupta and H Murrenhoff ldquoModelling and dynamicsof a servo-valve controlled hydraulic motor by bondgraphrdquoMechanism and Machine Theory vol 46 no 7 pp 1016ndash10352011

[32] Shi Jingzhuo and Zhang Jingsong ldquoA two-phase hybrid step-ping motor vector control servo systemrdquo Electric Machines andControl vol 4 no 3 pp 135ndash139 2000

[33] H-J Zhang L Quan and B Li ldquoPerformance of differentialcylinder position servo system controlled by permanentmagnetsynchronous motor driven pumprdquo Zhongguo Dianji GongchengXuebaoProceedings of the Chinese Society of Electrical Engineer-ing vol 30 no 24 pp 107ndash112 2010

[34] Deng Julong Wuhan Huazhong University of Science andTechnology 1993

Hindawiwwwhindawicom Volume 2018

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International Journal of Mathematics and Mathematical Sciences


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Volume 2018

Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom


4

R=300m

S1 S2

a 300 m diameter

instantaneous paraboloid

O

F=0467R1

23

56

7

89

120∘

120∘

Figure 1 The optical principle diagram of the active reflectorsystem 1 focusing surface 2 paraboloid 3 spherical surface 4triangular reflector unit 5 main cable net 6 cable net node 7 drop-down cable net 8 hydraulic actuator 9 anchor block

hydraulic actuators mentioned in this paper are all thesekinds of hydraulic actuators

The recent research on pump-controlled differentialcylinder mainly focuses on two aspects of modeling andcontrol strategy

For modeling in [11] the AMESim software is directlyused to model the whole hydraulic system rather thanfocusing on the mathematical description of the systemmodel In [12] a mathematical model of the hydraulic systemis established by state space equations but its research pointis the nonlinearity of friction force and the mathematicalmodel is relatively simple In this paper the hydraulicactuator system is modeled with the method of bond graphwhich not only considers the flow compensation due tothe asymmetry of hydraulic cylinder but also takes thecoupling of several energy domains into account A precisemathematical model of the hydraulic actuator is establishedeffectively

For the control strategy in [13 14] the nonlinear dynamicfeedforward compensation control strategy on the basis ofreforming the flow distribution principle of the pump orusing a special asymmetrical pump is proposed to improvethe dynamic and static performance of the differential cylin-der In [15 16] sliding mode control and robust Hinfin slidingmode control are developed which can achieve accuratetrajectory tracking and effectively resist external interferencebut the control object is the reformed single-rod cylinder notthe differential cylinder Moreover the control signal of slid-ing mode control cannot avoid the chattering which woulddamage themechanical system In [17 18] the neural networkis used as an identifier or a controller to the pump-controlleddifferential cylinder system to accelerate the convergencerate of the tracking error However after each operationthe weights of the neural network need to be updated suchcomplicated calculations make it unsuitable for engineeringpractice In this paper a switching grey prediction PID

control strategy is proposed which is not based on anymodification of system components Besides the interactionof several physical phenomena the uncertainty of the systemparameters the hysteresis and other nonlinear factors areconsidered comprehensively Grey system theory is particu-larly designed for handling situations in which only limiteddata are available especially as the system is not well-definedand fully understoodThe grey prediction technique has beensuccessfully employed to solve many engineering problemsincluding robot position control piezo-actuators positioncontrol which has the inherent hysteresis characteristic anonlinear liquid level system control and boiler drum levelcontrol [19ndash22] Therefore the goal of this control strategyis to apply grey theory to tune up the control parametersMoreover this paper describes a simpler scheme to changethe step size of the grey predictor which not only avoids thecomplexity that the step size is changed by the establishmentof fuzzy rules [23] but also avoids the inaccuracy that the stepsize is changed by step transform threshold set by experience[24]

In this paper the working principle and the integratedstructure of hydraulic actuator are designed for FAST projectSecondly its state space model is established by the methodof bond graphThen a switching grey prediction PID controlstrategy is designed according to the working conditions ofthe hydraulic actuator in the active reflector system In orderto verify the effectiveness of the whole control strategy notonly is simulation carried out on the basis of the bond graphmodel but also a field experiment platform is built in FASTand field tests are conducted

2 Hydraulic System of the Actuator

The hydraulic system is in the form of pump-controlledhydraulic differential cylinder whose working principle isshowed in Figure 2 [25] Apparently the unique system couldnot only meet the movement requirements of active reflectorsystem just by controlling the rod chamber of differentialhydraulic cylinder but also allow a variable transmissionof power by connecting a pump directly to an actuator[26]

21 Working Principle of Installation and Commissioning

211 Automatic Adjustment In this case there is no-loadAs the piston rod extends out the solenoid valves (DC1and DC2) are energized and the motor is reversed (counter-clockwise) so the rod chamber is connected to the nonrodchamber The oil supplied by the pump is combined withthe oil from rod chamber and then flows into the nonrodchamber to realize the output of the piston rod by usingdifferential output structure

When the piston rod is retracted DC1 and DC2 are offwhile the motor is also reversed The oil flows from the oiltank to the rod chamber passing through the pump and YDFOil in nonrod chamber flows back to the oil tank

212 Manual Adjustment In the absence of electricity thepiston rod can be extended or retracted at a certain speed


1

4

5

2

6Y1

Controller

8

TriangularReflector

Unit

B A

M

P

YL1

YL2

DC1 DC2

YDF

YL3

DF3 DF1 DF2 DF4

S2

S1

3

KB

7

9

drop-down cable net

FL











12

3 4 5 6 7 8 9 10

15

11 12

1314



Interface_2

Fiber interface

AC

filter

object instruction

solenoid valve


displacement sensor

Interface_1

Interface_3

Interface_4

CPUSTM

32F103Motor driving


stepping motor

coupling

gear pump


piston rod

external load

the temperature of

electrical chamber

the temperature

and pressure of oil












Stepping Motor

Gear Pump


PowerMechanical

PowerHydraulic

Power

Voltage (cause)

Torque (effect)

Pressure (effect)

Force (cause)

Current (effect)



Velocity (effect)

Effort variables

Flow variables

Mechanical Power




119880119860 = 119877119894119860 + 119871119889119894119860119889119905 minus 119911119903Φ119898120596119890 sin (119911119903120579119903)119880119861 = 119877119894119861 + 119871119889119894119861119889119905 + 119911119903Φ119898120596119890 cos (119911119903120579119903)

(1)



119879119890 = minus119911119903Φ119898119894119860sin (119911119903120579119903) + 119911119903Φ119898119894119861cos (119911119903120579119903) (2)


119879119890 = 119869119898 11988921205791199031198891199052 + 119861119898 119889120579119903119889119905 + 119879119871 (3)




RL fR

1MSe GY

mJ

outT

out


inQinp

outQoutp

tVn

T

Δp=poutminuspin



119876 = 119899119881119905 minus 119885VΔ119901 minus 119862V119889 (Δ119901)

119889119905119885V = 100381610038161003816100381610038161003816100381610038161003816

120597119876120597 (Δ119901)

100381610038161003816100381610038161003816100381610038161003816(4)



119879 = (11989631015840 + 1198811199052120587) Δ119901 minus 119887119899119899 minus 2120587119869119875119889119899119889119905

119887119899 = 120597119879120597119899

(5)


10MSe2

vRvC pL pR

outP

outQTF1

inT1

J wp R

(Vt2)in


epC

epCipC

1A

2A

1p

2p 1Q

2Q

px

lF




Δ119901119901 = 119870119901Δ119901 minus 119877119901119876119905 minus 119871119901 119889119876119905119889119905 (6)





1198761 = 1198601119901 + 119862119894119901 (1199011 minus 1199012) + 1198621198901199011199011 + 11988111205731198901198891199011119889119905


(7)


10inP

inQMSf

dC

tR

TF2

bR

m1s

F

pv0

(A2)Se



1198811 = 11986011199091199011198812 = 1198602 (119871 119904 minus 119909119901) (8)


11990111198601 minus 11990121198602 = 119898119901 + 119861119887119901 + 119865119897 (9)





1 0

dC

tR

TF2

bR

m

Se

1s

F

pv0

10

vRvC pL

pRTF1

RLfwR

MSe1 GY

J

1

2 3

4 5

6 7

8 9

10

12

1113

14

16

17

1819

20

21

2223

11


Motor Pump

ASRController

15

P

Q

SensorA

OB


Velocity

Target Value

+ +

minusminus

g

f

(A2)

(ke) (Vt2)





120579119894 (119905) = 119870120579 sdot int 119891 (119905) 119889119905 (11)




1198811010 = 11988111990521205871198691198756 minus 1119862V119877V

11988110 minus 11198711199011198751313 = 1

119862V11988110 minus 11987711990111987111990111987513 minus 1

1198621198891198811616 = 1

11987111990111987513 minus 111986211988911987711990511988116 minus 1198602119898 11987520

20 = 119860211986211988911988116 minus 119877119887119898 11987520 minus 119878119890

(12)






ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1


X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus



119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889


0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)


4 System Controller





(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887





























HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









1

4

5

2

6Y1

Controller

8

TriangularReflector

Unit

B A

M

P

YL1

YL2

DC1 DC2

YDF

YL3

DF3 DF1 DF2 DF4

S2

S1

3

KB

7

9

drop-down cable net

FL











12

3 4 5 6 7 8 9 10

15

11 12

1314



Interface_2

Fiber interface

AC

filter

object instruction

solenoid valve


displacement sensor

Interface_1

Interface_3

Interface_4

CPUSTM

32F103Motor driving


stepping motor

coupling

gear pump


piston rod

external load

the temperature of

electrical chamber

the temperature

and pressure of oil












Stepping Motor

Gear Pump


PowerMechanical

PowerHydraulic

Power

Voltage (cause)

Torque (effect)

Pressure (effect)

Force (cause)

Current (effect)



Velocity (effect)

Effort variables

Flow variables

Mechanical Power




119880119860 = 119877119894119860 + 119871119889119894119860119889119905 minus 119911119903Φ119898120596119890 sin (119911119903120579119903)119880119861 = 119877119894119861 + 119871119889119894119861119889119905 + 119911119903Φ119898120596119890 cos (119911119903120579119903)

(1)



119879119890 = minus119911119903Φ119898119894119860sin (119911119903120579119903) + 119911119903Φ119898119894119861cos (119911119903120579119903) (2)


119879119890 = 119869119898 11988921205791199031198891199052 + 119861119898 119889120579119903119889119905 + 119879119871 (3)




RL fR

1MSe GY

mJ

outT

out


inQinp

outQoutp

tVn

T

Δp=poutminuspin



119876 = 119899119881119905 minus 119885VΔ119901 minus 119862V119889 (Δ119901)

119889119905119885V = 100381610038161003816100381610038161003816100381610038161003816

120597119876120597 (Δ119901)

100381610038161003816100381610038161003816100381610038161003816(4)



119879 = (11989631015840 + 1198811199052120587) Δ119901 minus 119887119899119899 minus 2120587119869119875119889119899119889119905

119887119899 = 120597119879120597119899

(5)


10MSe2

vRvC pL pR

outP

outQTF1

inT1

J wp R

(Vt2)in


epC

epCipC

1A

2A

1p

2p 1Q

2Q

px

lF




Δ119901119901 = 119870119901Δ119901 minus 119877119901119876119905 minus 119871119901 119889119876119905119889119905 (6)





1198761 = 1198601119901 + 119862119894119901 (1199011 minus 1199012) + 1198621198901199011199011 + 11988111205731198901198891199011119889119905


(7)


10inP

inQMSf

dC

tR

TF2

bR

m1s

F

pv0

(A2)Se



1198811 = 11986011199091199011198812 = 1198602 (119871 119904 minus 119909119901) (8)


11990111198601 minus 11990121198602 = 119898119901 + 119861119887119901 + 119865119897 (9)





1 0

dC

tR

TF2

bR

m

Se

1s

F

pv0

10

vRvC pL

pRTF1

RLfwR

MSe1 GY

J

1

2 3

4 5

6 7

8 9

10

12

1113

14

16

17

1819

20

21

2223

11


Motor Pump

ASRController

15

P

Q

SensorA

OB


Velocity

Target Value

+ +

minusminus

g

f

(A2)

(ke) (Vt2)





120579119894 (119905) = 119870120579 sdot int 119891 (119905) 119889119905 (11)




1198811010 = 11988111990521205871198691198756 minus 1119862V119877V

11988110 minus 11198711199011198751313 = 1

119862V11988110 minus 11987711990111987111990111987513 minus 1

1198621198891198811616 = 1

11987111990111987513 minus 111986211988911987711990511988116 minus 1198602119898 11987520

20 = 119860211986211988911988116 minus 119877119887119898 11987520 minus 119878119890

(12)






ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1


X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus



119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889


0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)


4 System Controller





(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887





























HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









12

3 4 5 6 7 8 9 10

15

11 12

1314



Interface_2

Fiber interface

AC

filter

object instruction

solenoid valve


displacement sensor

Interface_1

Interface_3

Interface_4

CPUSTM

32F103Motor driving


stepping motor

coupling

gear pump


piston rod

external load

the temperature of

electrical chamber

the temperature

and pressure of oil












Stepping Motor

Gear Pump


PowerMechanical

PowerHydraulic

Power

Voltage (cause)

Torque (effect)

Pressure (effect)

Force (cause)

Current (effect)



Velocity (effect)

Effort variables

Flow variables

Mechanical Power




119880119860 = 119877119894119860 + 119871119889119894119860119889119905 minus 119911119903Φ119898120596119890 sin (119911119903120579119903)119880119861 = 119877119894119861 + 119871119889119894119861119889119905 + 119911119903Φ119898120596119890 cos (119911119903120579119903)

(1)



119879119890 = minus119911119903Φ119898119894119860sin (119911119903120579119903) + 119911119903Φ119898119894119861cos (119911119903120579119903) (2)


119879119890 = 119869119898 11988921205791199031198891199052 + 119861119898 119889120579119903119889119905 + 119879119871 (3)




RL fR

1MSe GY

mJ

outT

out


inQinp

outQoutp

tVn

T

Δp=poutminuspin



119876 = 119899119881119905 minus 119885VΔ119901 minus 119862V119889 (Δ119901)

119889119905119885V = 100381610038161003816100381610038161003816100381610038161003816

120597119876120597 (Δ119901)

100381610038161003816100381610038161003816100381610038161003816(4)



119879 = (11989631015840 + 1198811199052120587) Δ119901 minus 119887119899119899 minus 2120587119869119875119889119899119889119905

119887119899 = 120597119879120597119899

(5)


10MSe2

vRvC pL pR

outP

outQTF1

inT1

J wp R

(Vt2)in


epC

epCipC

1A

2A

1p

2p 1Q

2Q

px

lF




Δ119901119901 = 119870119901Δ119901 minus 119877119901119876119905 minus 119871119901 119889119876119905119889119905 (6)





1198761 = 1198601119901 + 119862119894119901 (1199011 minus 1199012) + 1198621198901199011199011 + 11988111205731198901198891199011119889119905


(7)


10inP

inQMSf

dC

tR

TF2

bR

m1s

F

pv0

(A2)Se



1198811 = 11986011199091199011198812 = 1198602 (119871 119904 minus 119909119901) (8)


11990111198601 minus 11990121198602 = 119898119901 + 119861119887119901 + 119865119897 (9)





1 0

dC

tR

TF2

bR

m

Se

1s

F

pv0

10

vRvC pL

pRTF1

RLfwR

MSe1 GY

J

1

2 3

4 5

6 7

8 9

10

12

1113

14

16

17

1819

20

21

2223

11


Motor Pump

ASRController

15

P

Q

SensorA

OB


Velocity

Target Value

+ +

minusminus

g

f

(A2)

(ke) (Vt2)





120579119894 (119905) = 119870120579 sdot int 119891 (119905) 119889119905 (11)




1198811010 = 11988111990521205871198691198756 minus 1119862V119877V

11988110 minus 11198711199011198751313 = 1

119862V11988110 minus 11987711990111987111990111987513 minus 1

1198621198891198811616 = 1

11987111990111987513 minus 111986211988911987711990511988116 minus 1198602119898 11987520

20 = 119860211986211988911988116 minus 119877119887119898 11987520 minus 119878119890

(12)






ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1


X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus



119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889


0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)


4 System Controller





(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887





























HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









Stepping Motor

Gear Pump


PowerMechanical

PowerHydraulic

Power

Voltage (cause)

Torque (effect)

Pressure (effect)

Force (cause)

Current (effect)



Velocity (effect)

Effort variables

Flow variables

Mechanical Power




119880119860 = 119877119894119860 + 119871119889119894119860119889119905 minus 119911119903Φ119898120596119890 sin (119911119903120579119903)119880119861 = 119877119894119861 + 119871119889119894119861119889119905 + 119911119903Φ119898120596119890 cos (119911119903120579119903)

(1)



119879119890 = minus119911119903Φ119898119894119860sin (119911119903120579119903) + 119911119903Φ119898119894119861cos (119911119903120579119903) (2)


119879119890 = 119869119898 11988921205791199031198891199052 + 119861119898 119889120579119903119889119905 + 119879119871 (3)




RL fR

1MSe GY

mJ

outT

out


inQinp

outQoutp

tVn

T

Δp=poutminuspin



119876 = 119899119881119905 minus 119885VΔ119901 minus 119862V119889 (Δ119901)

119889119905119885V = 100381610038161003816100381610038161003816100381610038161003816

120597119876120597 (Δ119901)

100381610038161003816100381610038161003816100381610038161003816(4)



119879 = (11989631015840 + 1198811199052120587) Δ119901 minus 119887119899119899 minus 2120587119869119875119889119899119889119905

119887119899 = 120597119879120597119899

(5)


10MSe2

vRvC pL pR

outP

outQTF1

inT1

J wp R

(Vt2)in


epC

epCipC

1A

2A

1p

2p 1Q

2Q

px

lF




Δ119901119901 = 119870119901Δ119901 minus 119877119901119876119905 minus 119871119901 119889119876119905119889119905 (6)





1198761 = 1198601119901 + 119862119894119901 (1199011 minus 1199012) + 1198621198901199011199011 + 11988111205731198901198891199011119889119905


(7)


10inP

inQMSf

dC

tR

TF2

bR

m1s

F

pv0

(A2)Se



1198811 = 11986011199091199011198812 = 1198602 (119871 119904 minus 119909119901) (8)


11990111198601 minus 11990121198602 = 119898119901 + 119861119887119901 + 119865119897 (9)





1 0

dC

tR

TF2

bR

m

Se

1s

F

pv0

10

vRvC pL

pRTF1

RLfwR

MSe1 GY

J

1

2 3

4 5

6 7

8 9

10

12

1113

14

16

17

1819

20

21

2223

11


Motor Pump

ASRController

15

P

Q

SensorA

OB


Velocity

Target Value

+ +

minusminus

g

f

(A2)

(ke) (Vt2)





120579119894 (119905) = 119870120579 sdot int 119891 (119905) 119889119905 (11)




1198811010 = 11988111990521205871198691198756 minus 1119862V119877V

11988110 minus 11198711199011198751313 = 1

119862V11988110 minus 11987711990111987111990111987513 minus 1

1198621198891198811616 = 1

11987111990111987513 minus 111986211988911987711990511988116 minus 1198602119898 11987520

20 = 119860211986211988911988116 minus 119877119887119898 11987520 minus 119878119890

(12)






ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1


X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus



119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889


0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)


4 System Controller





(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887





























HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









10MSe2

vRvC pL pR

outP

outQTF1

inT1

J wp R

(Vt2)in


epC

epCipC

1A

2A

1p

2p 1Q

2Q

px

lF




Δ119901119901 = 119870119901Δ119901 minus 119877119901119876119905 minus 119871119901 119889119876119905119889119905 (6)





1198761 = 1198601119901 + 119862119894119901 (1199011 minus 1199012) + 1198621198901199011199011 + 11988111205731198901198891199011119889119905


(7)


10inP

inQMSf

dC

tR

TF2

bR

m1s

F

pv0

(A2)Se



1198811 = 11986011199091199011198812 = 1198602 (119871 119904 minus 119909119901) (8)


11990111198601 minus 11990121198602 = 119898119901 + 119861119887119901 + 119865119897 (9)





1 0

dC

tR

TF2

bR

m

Se

1s

F

pv0

10

vRvC pL

pRTF1

RLfwR

MSe1 GY

J

1

2 3

4 5

6 7

8 9

10

12

1113

14

16

17

1819

20

21

2223

11


Motor Pump

ASRController

15

P

Q

SensorA

OB


Velocity

Target Value

+ +

minusminus

g

f

(A2)

(ke) (Vt2)





120579119894 (119905) = 119870120579 sdot int 119891 (119905) 119889119905 (11)




1198811010 = 11988111990521205871198691198756 minus 1119862V119877V

11988110 minus 11198711199011198751313 = 1

119862V11988110 minus 11987711990111987111990111987513 minus 1

1198621198891198811616 = 1

11987111990111987513 minus 111986211988911987711990511988116 minus 1198602119898 11987520

20 = 119860211986211988911988116 minus 119877119887119898 11987520 minus 119878119890

(12)






ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1


X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus



119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889


0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)


4 System Controller





(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887





























HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









1 0

dC

tR

TF2

bR

m

Se

1s

F

pv0

10

vRvC pL

pRTF1

RLfwR

MSe1 GY

J

1

2 3

4 5

6 7

8 9

10

12

1113

14

16

17

1819

20

21

2223

11


Motor Pump

ASRController

15

P

Q

SensorA

OB


Velocity

Target Value

+ +

minusminus

g

f

(A2)

(ke) (Vt2)





120579119894 (119905) = 119870120579 sdot int 119891 (119905) 119889119905 (11)




1198811010 = 11988111990521205871198691198756 minus 1119862V119877V

11988110 minus 11198711199011198751313 = 1

119862V11988110 minus 11987711990111987111990111987513 minus 1

1198621198891198811616 = 1

11987111990111987513 minus 111986211988911987711990511988116 minus 1198602119898 11987520

20 = 119860211986211988911988116 minus 119877119887119898 11987520 minus 119878119890

(12)






ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1


X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus



119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889


0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)


4 System Controller





(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887





























HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









ASRController

Sensor

Target Value

A

O

B

Displacement

Velocity

MSe1


X(t)

Y(t)or intY(t)dt

(X2(t)

J)

(int X4(t)

mdt)(X4(t)

m)

g

f

+ +

minus minus



119860 (119905) =

[[[[[[[[[[[[[[[[[[[[[

minus119877119871 minus119896119890119869 0 0 0 0

119896119890119871 minus119877119891119908119869 0 0 minus 1198811199052120587119862V0

0 0 minus119877119901119871119901 0 1119862Vminus 1119862119889


0 0 1119871119901 minus1198602119898 0 minus 1119862119889119877119905

]]]]]]]]]]]]]]]]]]]]]

119861 (119905) = [1 0 0 0 0 00 0 0 minus1 0 0]

119879

119862 (119905) = [0 0 0 1119898 0 0]119863 (119905) = 0

(14)


4 System Controller





(0) (119905 + 119898)= [119884(0) (119905 minus 119899 + 1) minus 119887





























HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018































HydraulicActuator


GM(11)

XPID controller

Y+

+

+

e(t)

e(t)

ec(t)minus

minus

minus

Y

u

E(t) EC(t)





Point2Point

200

400

600

Dis

plac

emen

t (m

m)

100 200 300 400 500 600 700 8000Time (s)

(a)

PIDSGPID

100 200 300 400 500 600 700 8000Time (s)

minus2

0

2

4

Velo

city

(mmmiddots-

)

(b)

0 100 200 300 400 500 600 700 800Time (s)

PIDSGPID

minus04minus02

002

Velo

city

Err

or (m

mmiddots-

)

(c)





Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









Target

0200400600800

10001200

Disp

lace

men

t (m

m)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

PIDSGPID

minus1

minus05

0

05

1

Erro

r (m

m)

(b)


Controller

Solenoid valve DC1



Solenoid valve DC2


Oil tank






(17)







0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018









0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

3Ve

loci

ty (m

mmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus04

minus02

0

02

04

Velo

city

Err

or (m

mmiddots-

)

(b)


0 500 1000 1500 2000 Time (s)minus2

minus1

0

1

2

Velo

city

(mmmiddots-

)

(a)

0 500 1000 1500 2000 Time (s)minus01

minus005

0

005

01

Velo

city

Err

or (m

mmiddots-

)

(b)


0 1000 2000 3000 4000 5000 6000 7000Time (s)

Target

0

500

1000

1500

Disp

lace

men

t (m

m)

(a)

0 1000 2000 3000 4000 5000 6000 7000Time (s)

minus1minus05

005

1

Erro

r (m

m)

PIDSGPID

(b)





7 Conclusion








Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018














Acknowledgments


References












































Journal of












Journal of







Volume 2018






Volume 2018






























Journal of












Journal of







Volume 2018






Volume 2018








Theoretical and Experimental Analysis of the Hydraulic...

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Transcript of Theoretical and Experimental Analysis of the Hydraulic...